Toothpick Patterns

Sixth Grade Poster Problem
Expressions and Equations

This problem helps to bridge the gap in student thinking from a concrete pattern or story to a generalized, abstract arithmetic expression or formula.

By the end of this problem, students will generate equations showing the number of toothpicks in a pattern that grows linearly. Since there are many ways to look at this problem, students might come up with equations that look different but actually result in the same values. When this situation happens, we say that the equations are equivalent. You have a vital role highlighting two important concepts: that equivalent expressions exist, and that we can simplify expressions.

Learning Objectives:

  • Write, read, and evaluate expressions in which letters stand for numbers.
  • Apply the properties of operations to generate equivalent expressions.
  • Identify when two expressions are equivalent.
  • Use variables to represent two quantities in a real-world problem that change in relationship to one another.

Common Core State Standards for Mathematics:

The Lesson Plan:

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Project funding provided by The William and Flora Hewlett Foundation and S.D. Bechtel Jr. Foundation.

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